Find $$x$$ if $$\sin x = -\frac{1}{2}$$

Given, $$\sin x = -\frac{1}{2}$$

$$\sin x$$ is negative in third and fourth quadrant

$$\Rightarrow$$  $$\sin x=-\sin30^{\circ\ }$$

$$\Rightarrow$$  $$\sin x=\sin\left(180+30\right)^{\circ\ }$$   or   $$\sin x=\sin\left(360-30\right)^{\circ\ }$$

$$\Rightarrow$$  $$x=210^{\circ\ }$$    or   $$x=330^{\circ\ }$$

$$\Rightarrow$$  $$x=210\times\frac{\pi\ }{180}$$  or  $$x=330\times\frac{\pi\ }{180}$$

$$\Rightarrow$$  $$x=\frac{7\pi\ }{6}$$  or  $$x=\frac{11\pi\ }{6}$$

Hence, the correct answer is Option B